Problem: Simplify the following expression: $k = \dfrac{2f^2 + 6f}{hf - 4f^2} + \dfrac{6f^2 - 4f}{hf - 4f^2}$ You can assume $f,g,h \neq 0$.
Solution: Since the expressions have the same denominator we simply combine the numerators: $k = \dfrac{2f^2 + 6f + 6f^2 - 4f}{hf - 4f^2}$ $k = \dfrac{8f^2 + 2f}{hf - 4f^2}$ The numerator and denominator have a common factor of $f$, so we can simplify $k = \dfrac{8f + 2}{h - 4f}$